mathjs/src/type/complex/function/complex.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict'

const deepMap = require('../../../utils/collection/deepMap')

function factory (type, config, load, typed) {
  const latex = require('../../../utils/latex')

  /**
   * Create a complex value or convert a value to a complex value.
   *
   * Syntax:
   *
   *     math.complex()                           // creates a complex value with zero
   *                                              // as real and imaginary part.
   *     math.complex(re : number, im : string)   // creates a complex value with provided
   *                                              // values for real and imaginary part.
   *     math.complex(re : number)                // creates a complex value with provided
   *                                              // real value and zero imaginary part.
   *     math.complex(complex : Complex)          // clones the provided complex value.
   *     math.complex(arg : string)               // parses a string into a complex value.
   *     math.complex(array : Array)              // converts the elements of the array
   *                                              // or matrix element wise into a
   *                                              // complex value.
   *     math.complex({re: number, im: number})   // creates a complex value with provided
   *                                              // values for real an imaginary part.
   *     math.complex({r: number, phi: number})   // creates a complex value with provided
   *                                              // polar coordinates
   *
   * Examples:
   *
   *    const a = math.complex(3, -4)     // a = Complex 3 - 4i
   *    a.re = 5                          // a = Complex 5 - 4i
   *    const i = a.im                    // Number -4
   *    const b = math.complex('2 + 6i')  // Complex 2 + 6i
   *    const c = math.complex()          // Complex 0 + 0i
   *    const d = math.add(a, b)          // Complex 5 + 2i
   *
   * See also:
   *
   *    bignumber, boolean, index, matrix, number, string, unit
   *
   * @param {* | Array | Matrix} [args]
   *            Arguments specifying the real and imaginary part of the complex number
   * @return {Complex | Array | Matrix} Returns a complex value
   */
  const complex = typed('complex', {
    '': function () {
      return type.Complex.ZERO
    },

    'number': function (x) {
      return new type.Complex(x, 0)
    },

    'number, number': function (re, im) {
      return new type.Complex(re, im)
    },

    // TODO: this signature should be redundant
    'BigNumber, BigNumber': function (re, im) {
      return new type.Complex(re.toNumber(), im.toNumber())
    },

    'Complex': function (x) {
      return x.clone()
    },

    'string': function (x) {
      return type.Complex(x) // for example '2 + 3i'
    },

    'null': function (x) {
      return type.Complex(0)
    },

    'Object': function (x) {
      if ('re' in x && 'im' in x) {
        return new type.Complex(x.re, x.im)
      }

      if (('r' in x && 'phi' in x) || ('abs' in x && 'arg' in x)) {
        return new type.Complex(x)
      }

      throw new Error('Expected object with properties (re and im) or (r and phi) or (abs and arg)')
    },

    'Array | Matrix': function (x) {
      return deepMap(x, complex)
    }
  })

  complex.toTex = {
    0: '0',
    1: `\\left(\${args[0]}\\right)`,
    2: `\\left(\\left(\${args[0]}\\right)+${latex.symbols['i']}\\cdot\\left(\${args[1]}\\right)\\right)`
  }

  return complex
}

exports.name = 'complex'
exports.factory = factory